Two consecutive positive integers have a product of 6. what are the integers

Hey there!

One way to do this is find all the factors of 6 and then see which pair fit the requirements.

The factors of 6 are 1, 2, 3, and 6. (Note: There can be negative factors, but I am going to leave them out since it is asking for positive integers.)

You can find them by asking if each number can go into 6.

1, 2, 3, and 6 all go into 6, while 4 and 5 do not.

The requirements we have is that they must be consecutive and have a product of 6.

Consecutive means right after one another.

The only numbers that fit this are 2 and 3.

2 x 3 = 6

Hope this helps!

2,3

Step-by-step explanation:

Consecutive means in a row, so x and x+1

x(x+1) = 6

Distribute

x^2 +x = 6

Subtract 6 from each side

x^2 +x - 6 =0

Factor

(x+3) (x-2) =0

Using the zero product property

x=-3, x=2

We only want positive integers

x=2

x+1 =3

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